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Sequential Convex Programming for Multimode Spacecraft Trajectory Optimization

Jack Yarndley

TL;DR

The paper tackles optimal design of multimode, multi-propulsion spacecraft trajectories, where discrete propulsion modes and nonlinear dynamics complicate optimization. It introduces a sequential convex programming (SCP) framework that extends dynamic linearization with sparse automatic differentiation to efficiently incorporate many propulsion modes, plus lossless convexification for solar sails and novel constraints to enforce a single active mode per time step and limit total modes. The objective maximizes final mass while penalizing soft feasibility controls; the method uses segment-wise discretization, forward-mode AD, and a sparsity-aware Jacobian computation with matrix coloring. Two case studies—Earth–67P rendezvous with SPT-140 and Earth–Mars transfer with SEP and solar sail—demonstrate accurate, computationally efficient trajectory solutions and informative mode usage patterns. The results suggest substantial design flexibility for future missions employing multimode propulsion.

Abstract

Spacecraft equipped with multiple propulsion modes or systems can offer enhanced performance and mission flexibility compared with traditional configurations. Despite these benefits, the trajectory optimization of spacecraft utilizing such configurations remains a complex challenge. This paper presents a sequential convex programming (SCP) approach for the optimal design of multi-mode and multi-propulsion spacecraft trajectories. The method extends the dynamical linearization within SCP using sparse automatic differentiation, enabling efficient inclusion of multiple propulsion modes or systems without complex manual reformulation while maintaining comparable computational efficiency. New constraint formulations are introduced to ensure selection of a single propulsion mode at each time step and limit the total number of modes used. The approach is demonstrated for (i) a low-thrust Earth-67P rendezvous using the SPT-140 thruster with 20 discrete modes, and (ii) an Earth-Mars transfer employing both a low-thrust engine and a solar sail. Results confirm that the proposed method can efficiently compute optimal trajectories for these scenarios.

Sequential Convex Programming for Multimode Spacecraft Trajectory Optimization

TL;DR

The paper tackles optimal design of multimode, multi-propulsion spacecraft trajectories, where discrete propulsion modes and nonlinear dynamics complicate optimization. It introduces a sequential convex programming (SCP) framework that extends dynamic linearization with sparse automatic differentiation to efficiently incorporate many propulsion modes, plus lossless convexification for solar sails and novel constraints to enforce a single active mode per time step and limit total modes. The objective maximizes final mass while penalizing soft feasibility controls; the method uses segment-wise discretization, forward-mode AD, and a sparsity-aware Jacobian computation with matrix coloring. Two case studies—Earth–67P rendezvous with SPT-140 and Earth–Mars transfer with SEP and solar sail—demonstrate accurate, computationally efficient trajectory solutions and informative mode usage patterns. The results suggest substantial design flexibility for future missions employing multimode propulsion.

Abstract

Spacecraft equipped with multiple propulsion modes or systems can offer enhanced performance and mission flexibility compared with traditional configurations. Despite these benefits, the trajectory optimization of spacecraft utilizing such configurations remains a complex challenge. This paper presents a sequential convex programming (SCP) approach for the optimal design of multi-mode and multi-propulsion spacecraft trajectories. The method extends the dynamical linearization within SCP using sparse automatic differentiation, enabling efficient inclusion of multiple propulsion modes or systems without complex manual reformulation while maintaining comparable computational efficiency. New constraint formulations are introduced to ensure selection of a single propulsion mode at each time step and limit the total number of modes used. The approach is demonstrated for (i) a low-thrust Earth-67P rendezvous using the SPT-140 thruster with 20 discrete modes, and (ii) an Earth-Mars transfer employing both a low-thrust engine and a solar sail. Results confirm that the proposed method can efficiently compute optimal trajectories for these scenarios.

Paper Structure

This paper contains 8 sections, 14 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Dynamics and propulsion models
  4. Sequential convex programming
  5. Results and Discussion
  6. Earth-67P rendezvous with SPT-140 thruster
  7. Earth-Mars transfer with two different propulsion technologies
  8. Conclusions

Figures (5)

  • Figure 1: Structure and colors assigned to the Jacobian matrix.
  • Figure 2: Optimal Earth-67P trajectory with all 20 modes of the SPT-140 thruster.
  • Figure 3: Control and power profiles for the Earth-67P mission.
  • Figure 4: Optimal Earth-Mars trajectory with SEP and solar sail.
  • Figure 5: Final mass of Earth-Mars mission with differing sail area-to-mass ratios.